Question
Which of the following is an antiderivative of
(A)
(B)
(D)
(E)
(D)
(A)
(B)
(D)
(E)
(D)
Ask by Summers Byrd. in the United States
Jan 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The antiderivative is
Solution
To find an antiderivative of the function
-
Integrate
: (Recall that the derivative ofis .) -
Integrate
:
Combining both results, the general antiderivative is:
where
Among the provided options, option (B) matches this antiderivative:
(B)
Answer: Option (B)
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To find the antiderivative of
Now, let’s make this even more fun! Did you know that the secant function is the reciprocal of the cosine function? So when you’re finding the integral involving secants, you’re really diving into the deep waters of trigonometric identities!
Also, if you ever get stuck while integrating, remember to have a checklist: check for basic derivatives, see if you can factor out constants, and don’t forget about the power rule for polynomials. Mistakes often happen when the terms are mismanaged, so clear organization is key!
